1. Objective / Мета роботи #

Understand and implement the Cartesian product of sets and the related operations on binary relations.

By the end of the work the student should be able to:

• construct the Cartesian product $A \times B$ of two finite sets as the set of all ordered pairs $(a, b)$ with $a \in A$ and $b \in B$, using only basic data structures;
• explain a binary relation as a subset of $A \times B$, and validate whether a given list of ordered pairs is a legitimate relation for two sets;
• generate a relation on a set from a predicate (relation function), such as a divisibility rule;
• filter a Cartesian product to the pairs that satisfy a supplied condition;
• reason about the size of a product ($|A \times B| = |A|\cdot|B|$) and about the time complexity of each operation.

The work builds directly on the set operations of Laboratory Work 1 and prepares the ground for the study of relations, functions, and graphs later in the course.

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